Multivariate regression for pivot selection: A preliminary study

Abstract

Pivot selection partially dominates the query performance of pivot-based metric space indexing methods. Lacking of coordinate system in metric spaces, mathematical tools for Rn had been prevented from being applied to metric spaces. The pivot space model embeds a metric space into a high dimensional space while preserving all the pair-wise distances. As a result, pivot selection turns into a special form of dimension reduction which only selects existing dimensions. Given a set of predictors and a response variable, multivariate regression finds a subset of predictors to predict the response variable. Considering dimensions as predictors and artificially specifying the response variable, we show how multivariate regression methods can be applied to pivot selection. Empirical results show that regression methods have comparable query performance with the commonly used corner selection heuristic, although not as good as the PCA-based method. As a preliminary study, this paper demonstrates a new possible research direction of pivot selection.